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On (k, l)-sets in cyclic groups of odd prime order

Published online by Cambridge University Press:  17 April 2009

T. Bier  and
A. Y. M. Chin
T. Bier
Affiliation:
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia, e-mail: [email protected], [email protected]
A. Y. M. Chin
Affiliation:
Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia, e-mail: [email protected], [email protected]
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Abstract

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Let A be a finite Abelian group written additively. For two positive integers k, l with k ≠ l, we say that a subset S ⊂ A is of type (k, l) or is a (k, l) -set if the equation x1 + x2 + … + xk − xk+1−… − xk+1 = 0 has no solution in the set S. In this paper we determine the largest possible cardinality of a (k, l)-set of the cyclic group ℤP where p is an odd prime. We also determine the number of (k, l)-sets of ℤp which are in arithmetic progression and have maximum cardinality.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 115 - 121
Copyright
Copyright © Australian Mathematical Society 2001

References

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